It is said that each observable like position or momentum is represented by a Hermitian operator acting on the state space. And the Hamiltonian is the total energy of the system, kinetic and potential.. so it means the Hamiltonians encode or encompass the energy of all observables (like position, spin, charges, momentum, etc.) at the same instance? Or do you analyze each Hamiltonian separately for each observable and add them together? Second inquiry. In Wikipedia it is stated that "As it turns out, analytic solutions of the Schrödinger equation are available for only a very small number of relatively simple model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion, and the hydrogen atom are the most important representatives. Even the helium atom - which contains just one more electron than does the hydrogen atom - has defied all attempts at a fully analytic treatment.". Does it mean we can only get the complete Hamiltonian (combination of all observables) for only hydrogen atom and barely for helium? Meaning there is no way to get the Hamiltonian of molecules?